There are many prior art techniques for determining and mapping impedance of subsurface areas. In most of these techniques a plurality of acoustic signal sources direct signals into the earth toward a common depth point (CDP). This process is known as "stacking". A portion of each signal is reflected back when it reaches an interface between two subsurface strata or layers of differing impedance. The signals that are reflected back are picked up by receivers at the surface and the amplitudes of those signals can be used to determine reflectivity or reflection coefficients at the interfaces between subsurface layers of differing impedance.
The time between transmission of the acoustic signals to reception of the reflected portion of the signals is called "two way" time. In seismic data charts amplitude of a received signal is plotted versus two way time. A single vertical signal line on a seismic chart is called a "trace." A trace is essentially one dimensional showing signal amplitudes or reflectivity data of a plurality of vertical layers at a single horizontal position. A trace can be in wavelet form which is a continuous function showing positive and negative amplitudes, or in spiked signal form. Because the reflectivity of an interface is related to the impedance of the two vertically adjacent layers which form the interface, knowing the impedance of one layer and the reflectivity of the interface allows one to calculate the impedance of the vertically adjacent layer. The process requires inversion of the reflectivity data. Prior art techniques need to perform a wavelet estimation, which means changing the continuous wave seismic data to spiked seismic data.
While most impedance mapping techniques use reflectivity data, these techniques differ in how they process these data.
One well known prior art approach for mapping impedance characteristics is called a "recursive" approach. In this approach the impedance characteristics at a particular horizontal position of one subsurface layer are determined from a received signal amplitude from the interface between two vertically adjacent layers and the knowledge of the impedance of one of the two layers. The impedance of the determined layer at the determined horizontal position is then used to calculate the impedance at the same horizontal position for a subsurface layer below, in the same manner. In order to obtain impedance data concerning a large lateral section, several traces are used.
Another approach which has been used to determine impedance characteristics is a trace by trace modelling approach. Such an approach is described in "Generalized Linear Inversion of Reflection Data", Cooke Geophysics, Vol 48, No 6, June 1983 (pp. 665-676). In this approach, an initial impedance model is provided for a particular trace, using for example well impedance data. That model is updated until the modelled seismic response is within a given error of the actual "trace" from reflected signals. After impedance characteristics for an entire trace have been determined, the next trace is modelled and updated to within an error of the actual seismic data.
Both recursive and "trace by trace" prior art modelling techniques can be said to map impedance vertically, trace by trace.
Some model based apparatus, such as SLIM (Seismic Lithologic Modeling) develop an initial model of multiple traces and then update these models. However, these multiple trace apparatus operate on an entire two-dimensional section of a plurality of subsurface layers.
In all model based apparatus, an initial model is provided then updated through multiple iterations, to reach a solution. Such iterative algorithms have to deal with convergence and nonuniqueness issues because of the non-linear nature of "inversion".
All prior art techniques whether recursive or modelling treat reflectivity in the vertical direction.